The Berezinskii-Kosterlitz-Thouless (BKT) phase transition is considered in the condition of lowest temperatures, when thermal fluctuations give place to quantum ones. For this goal, the critical dynamic of the Sine-Gordon model near the quantum critical point is considered. The approach based on the Keldysh-Schwinger technique of non-equilibrium dynamics description is used, as well as the method of taking into account the crossover from the thermal fluctuation regime to the quantum one in the renormalization group technique. For the system with low vortex concentration, it is shown that the BKT transition unavoidably occurs at a temperature above the crossover temperature from the thermal fluctuation regime to quantum one. As a result at small temperatures the critical exponent of the BKT transition, $η=1/4$ , remains unchanged, however, the universal relation of the superfluid density jump adjusts a little from the well-known relation by Nelson and Kosterlitz.The Berezinskii-Kosterlitz-Thouless (BKT) phase transition is considered in the condition of lowest temperatures, when thermal fluctuations give place to quantum ones. For this goal, the critical dynamic of the Sine-Gordon model near the quantum critical point is considered. The approach based on the Keldysh-Schwinger technique of non-equilibrium dynamics description is used, as well as the method of taking into account the crossover from the thermal fluctuation regime to the quantum one in the renormalization group technique. For the system with low vortex concentration, it is shown that the BKT transition unavoidably occurs at a temperature above the crossover temperature from the thermal fluctuation regime to quantum one. As a result at small temperatures the critical exponent of the BKT transition, $η=1/4$, remains unchanged, however, the universal relation of the superfluid density jump adjusts a little from the well-known relation by Nelson and Kosterlitz.

arXiv:2104.10983Apr 22, 20210 citations

Non-equilibrium Relaxation Analysis of Kosterlitz-Thouless Phase Transition

之康尾関, Yukiyasu Ozeki

Jan 1, 20010 citations

Universal coarsening of a two-dimensional Bose gas under conservative evolution

Andrew J. Groszek, T. P. Billam

We investigate the phase ordering dynamics of a uniform two-dimensional Bose gas quenched to a finite temperature in the superfluid phase. Starting from a defect-rich, far-from-equilibrium state, we model the subsequent evolution with the projected Gross-Pitaevskii equation, which conserves both energy and particle number. By tuning the initial energy, we control the effective post-quench temperature and examine its role in the equilibration dynamics. We find that the gas exhibits universal behaviour at all temperatures, evidenced by spatio-temporal scaling of correlation functions and power-law growth of the correlation length $\sim t^{1/z}$ , with $z$ the dynamical critical exponent. We find $z$ to be temperature dependent, with $z \approx 1.5$ for post-quench temperatures just below the Berezinskii-Kosterlitz-Thouless (BKT) transition, and $z \approx 1.9$ for quenches to near-zero temperature. Analysis of the Porod tail of the momentum distribution suggests a temperature-dependent competition between vortices and sound waves in the coarsening process. The two-time correlation function also exhibits universal scaling, decaying as $\sim t^{-λ/z}$ , with autocorrelation exponent $λ$ . Near the BKT transition we obtain $λ\approx 2$ , whereas $λ$ is found to diverge as the effective temperature approaches zero.We investigate the phase ordering dynamics of a uniform two-dimensional Bose gas quenched to a finite temperature in the superfluid phase. Starting from a defect-rich, far-from-equilibrium state, we model the subsequent evolution with the projected Gross-Pitaevskii equation, which conserves both energy and particle number. By tuning the initial energy, we control the effective post-quench temperature and examine its role in the equilibration dynamics. We find that the gas exhibits universal behaviour at all temperatures, evidenced by spatio-temporal scaling of correlation functions and power-law growth of the correlation length $\sim t^{1/z}$, with $z$ the dynamical critical exponent. We find $z$ to be temperature dependent, with $z \approx 1.5$ for post-quench temperatures just below the Berezinskii-Kosterlitz-Thouless (BKT) transition, and $z \approx 1.9$ for quenches to near-zero temperature. Analysis of the Porod tail of the momentum distribution suggests a temperature-dependent competition between vortices and sound waves in the coarsening process. The two-time correlation function also exhibits universal scaling, decaying as $\sim t^{-λ/z}$, with autocorrelation exponent $λ$. Near the BKT transition we obtain $λ\approx 2$, whereas $λ$ is found to diverge as the effective temperature approaches zero.

arXiv:2601.02687Jan 6, 20260 citations

Superfluid density and critical velocity near the Berezinskii-Kosterlitz-Thouless transition in a two-dimensional strongly interacting Fermi gas

Brendan C. Mulkerin, Lianyi He, Paul Dyke +3 more

We theoretically investigate superfluidity in a strongly interacting Fermi gas confined to two dimensions at finite temperature. Using a Gaussian pair fluctuation theory in the superfluid phase, we calculate the superfluid density and determine the critical temperature and chemical potential at the Berezinskii-Kosterlitz-Thouless transition. We propose that the transition can be unambiguously demonstrated in cold-atom experiments by stirring the superfluid Fermi gas using a red-detuned laser beam, to identify the characteristic jump in the local Landau critical velocity at the superfluid-normal interface, as the laser beam moves across the cloud.We theoretically investigate superfluidity in a strongly interacting Fermi gas confined to two dimensions at finite temperature. Using a Gaussian pair fluctuation theory in the superfluid phase, we calculate the superfluid density and determine the critical temperature and chemical potential at the Berezinskii-Kosterlitz-Thouless transition. We propose that the transition can be unambiguously demonstrated in cold-atom experiments by stirring the superfluid Fermi gas using a red-detuned laser beam, to identify the characteristic jump in the local Landau critical velocity at the superfluid-normal interface, as the laser beam moves across the cloud.

arXiv:1702.07091Physical Review ANov 6, 201731 citations

Numerical Study of Critical Exponents for Kosterlitz-Thouless Transition Systems

Yukiyasu Ozeki, Nobuyasu Ito

Springer proceedings in physicsJan 1, 20044 citations

η=1/4

, remains unchanged, however, the universal relation of the superfluid density jump adjusts a little from the well-known relation by Nelson and Kosterlitz.

\sim t^{1/z}

, with

z

the dynamical critical exponent. We find

z

to be temperature dependent, with

z \approx 1.5

for post-quench temperatures just below the Berezinskii-Kosterlitz-Thouless (BKT) transition, and

z \approx 1.9

for quenches to near-zero temperature. Analysis of the Porod tail of the momentum distribution suggests a temperature-dependent competition between vortices and sound waves in the coarsening process. The two-time correlation function also exhibits universal scaling, decaying as

\sim t^{-λ/z}

, with autocorrelation exponent

λ

. Near the BKT transition we obtain

λ\approx 2

, whereas

λ

is found to diverge as the effective temperature approaches zero.